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A321334
n such that all n - s are squarefree numbers where s is a squarefree number in range n/2 <= s < n.
0
2, 3, 4, 5, 6, 7, 8, 12, 13, 16, 36
OFFSET
1,1
COMMENTS
The following is a quotation from Hage-Hassan in his paper (see Link below). "The (concept of) right and left symmetry is fundamental in physics. This incites us to ask whether this symmetry is in (the) primes. Find the numbers n with a + a' = n. a, a' are primes and {a} are all the primes with: n/2 <= a < n and n = 2,3, ..."
This sequence is analogous to A320447. Instead of the sequence of primes it uses the sequence of squarefree numbers (A005117). It is conjectured that the sequence is finite and full.
LINKS
EXAMPLE
a(10)=16, because the squarefree numbers s in the range 8 <= s < 16 are {10, 11, 13, 14, 15}. Also the complementary set {6, 5, 3, 2, 1} has all its members practical numbers. This is the 10th occurrence of such a number.
MATHEMATICA
plst[n_] := Select[Range[Ceiling[n/2], n-1], SquareFreeQ]; lst={}; Do[If[plst[n]!={}&&AllTrue[n-plst[n], SquareFreeQ], AppendTo[lst, n]], {n, 1, 10000}]; lst
CROSSREFS
Sequence in context: A032972 A210585 A240082 * A342044 A238084 A211202
KEYWORD
nonn,more
AUTHOR
Frank M Jackson, Dec 18 2018
STATUS
approved